A209671 a(n) = count of monomials, of degree k=n, in the elementary symmetric polynomials e(mu,k) summed over all partitions mu of n.

1, 5, 37, 405, 5251, 84893, 1556535, 33175957, 785671039, 20841132255, 604829604655, 19236214748061, 661348833658423, 24554370466786319, 976242978063976162, 41477168810872793493, 1872694395510428040983, 89644070894632864643651, 4531712537608857605836563

Offset: 1

Author

Wouter Meeussen, Mar 11 2012

Keywords

• nonn

Links

• Peter J. Taylor, Table of n, a(n) for n = 1..100
• Wikipedia, Symmetric Polynomials

Crossrefs

Cf. A209664-A209673.

Programs

Mathematica

e[n_, v_] := Tr[Times @@@ Select[Subsets[Table[Subscript[x, j], {j, v}]], Length[#] == n &]]; e[par_?PartitionQ, v_] := Times @@ (e[#, v] & /@ par); Tr /@ Table[(e[#, l] & /@ Partitions[l]) /. Subscript[x, _] -> 1, {l, 10}]

Formula

Main diagonal of triangle A209669.

Extensions

More terms from Peter J. Taylor, Mar 02 2017